Detection of singularities using segment approximation

Grothmann, R.; Mhaskar, H. N.

doi:10.1090/S0025-5718-1992-1145662-2

Detection of singularities using segment approximation
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by R. Grothmann and H. N. Mhaskar PDF

Math. Comp. 59 (1992), 533-540 Request permission

Abstract:

We discuss best segment approximation (with free knots) by polynomials to piecewise analytic functions on a real interval. It is shown that, if the degree of the polynomials tends to infinity and the number of knots is the same as the number of singularities of the function, then the optimal knots converge geometrically fast to the singularities. When the degree is held fixed and the number of knots tends to infinity, we study the asymptotic distribution of the optimal knots.

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